2000 Sonata GLS V6 failsafe limp mode issues
 

These last few months have been a nightmare with my Sonata! Let me give some background:

This last summer I replaced the A/C compressor after several years of it not working. Almost immediately the car started giving a sharp jerk when the A/C was on. I assumed it was probably just the clutch engaging and ignored it. Well, about a month ago the car started stalling (engine would just shut off) occasionally when stopped at an intersection. Soon it turned into jolting really sharply while driving (I would briefly get a check engine light for about 1 or 2 seconds and then it would turn off. No codes were stored) and still stalling at intersections. After replacing the fuel filter, MAF sensor and input speed sensor I finally got two codes (P0755 and p0760). At this point it was time to take it in to the mechanic. My torque converter was destroyed and I needed a transmission rebuild (yay). The car came back and I have to admit the transmission feels nice. I don't think shifting has ever been so smooth.

But.... while driving I am still getting a good jolt and now the car is going into fail safe (limp) mode. I have now replaced the throttle position switch and and the idle air control valve. Still no joy. It seems the problem occurs the most the more electronic components I'm running (headlights, A/C, rear defroster, etc.). The problem is intermittent and still no check engine light. I've been able to go on a few 30+ mile trips with no problems, but it has also had the problem 1/4 mile from my house. Now I'm completely at a loss (and out of money) and could use some ideas. On a side note, my tachometer hasn't worked for some time now so I have no idea how many RPM when this happens or even if that would matter. Thanks in advance!

OK, this is just weird... simply because I've run out of parts to check, I brought my car to autozone and had the battery tested. They said my battery was bad and seemed to be a little high on voltage. Fortunately the battery was still under warranty and they swapped it out no problem. I just changed the alternator a few month ago and think that it is running fine.

Now I've taken the car on several test drives and it seems to be doing fine (although I might be jumping the gun again on the victory dance). The only thing I can't figure out is, how can a battery cause intermittent stalling and fail-safe mode to come on? If it really is fixed I'm not complaining and I will accept "magic" as an answer, but I would like it to make a little more sense than that.